Enigmatic Code
Programming Enigma Puzzles
BrainTwister #26: Up and down
Posted by on 27 June 2024
From New Scientist #3497, 29th June 2024 [link] [link]
Which is bigger, 30 × 30 or 29 × 31?
If we choose a number other than 30 and compare its product with itself to the product of the numbers one above and one below it, which is bigger? Does this always work the same way?
If you choose any two numbers that are above and below 30 by the same amount, what is the difference between their product and 30 × 30?
[braintwister26]
Enigmatic Code 
If we consider the “difference of two squares” formula:
If y = 0 the result is x².
If y = 1 the result is x² − 1, so it is always smaller than the previous result.
And in general for y > 0 the result x² − y² is always less than x².
So, the answer to the last question is y**2.
@ruud: That’s right.
Here’s the ‘proof’:
from sympy import expand, symbols x, y = symbols('x y') print(expand((30 * 30) - (30 + y) * (30 - y)))Output: